In every base you use to move to the next larger place you must multiply the previous number by the base.
Henceforth, base 2 is written as 1, 2, 4, 8, 16, 32…
Base 3 is written as 1, 3, 9, 27…
Base 4 is written as 1, 4, 16…
Base 5 is written as 1, 5, 25…
Base 6 is written as 1, 6, 36…
Base 7 is written as 1, 7, 49…
Base 8 is written as 1, 8, 64…
Base 9 is written as 1, 9, 81…
And base 10 (our ever-reliable decimal system) goes 1, 10, 100...
Here is an example at how you can create a single number in the different bases:
Number
Base
What it looks like
45
10 (Decimal System)
45
45
2
1011012
45
3
12003
45
4
1714
45
5
1405
45
6
1136
45
7
637
45
8
458
45
9
509
But how does it work, you might ask?
Here’s how:
Base 2:
1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1 = 45
Base 3:
1x27 + 1x9 + 0x3 + 0x1 = 45
Base 4:
1x16 + 7x4 + 1x1 = 45
Base 5:
1x25 + 4x5 + 0x1 = 45
Base 6:
1x36 + 1x6 + 1x3 = 45
Base 7:
6x7 + 3x1 = 45
Base 8:
4x8 + 5x1 = 45
Base 9:
5x9 + 0x1 = 45 Numbers in bases are always written largest number first.
Henceforth, base 2 is written as 1, 2, 4, 8, 16, 32…
Base 3 is written as 1, 3, 9, 27…
Base 4 is written as 1, 4, 16…
Base 5 is written as 1, 5, 25…
Base 6 is written as 1, 6, 36…
Base 7 is written as 1, 7, 49…
Base 8 is written as 1, 8, 64…
Base 9 is written as 1, 9, 81…
And base 10 (our ever-reliable decimal system) goes 1, 10, 100...
Here is an example at how you can create a single number in the different bases:
But how does it work, you might ask?
Here’s how:
Base 2:
1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1 = 45
Base 3:
1x27 + 1x9 + 0x3 + 0x1 = 45
Base 4:
1x16 + 7x4 + 1x1 = 45
Base 5:
1x25 + 4x5 + 0x1 = 45
Base 6:
1x36 + 1x6 + 1x3 = 45
Base 7:
6x7 + 3x1 = 45
Base 8:
4x8 + 5x1 = 45
Base 9:
5x9 + 0x1 = 45
Numbers in bases are always written largest number first.